A 2-stage strategy updating rule promotes cooperation in the prisoner's dilemma game

doi:10.1088/1674-1056/21/10/108702

中国物理B ›› 2012, Vol. 21 ›› Issue (10): 108702-108702.doi: 10.1088/1674-1056/21/10/108702

• INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY • 上一篇下一篇

A 2-stage strategy updating rule promotes cooperation in the prisoner's dilemma game

方祥圣^a, 朱平^b, 刘润然^c, 刘恩钰^d, 魏贵义^b

a Department of Information Science, Anhui Institute of Economic Management, Hefei 230059, China;
b Networking and Distributed Computing Laboratory, Zhejiang Gongshang University, Hangzhou 310018, China;
c Institute for Information Economy, Hangzhou Normal University, Hangzhou 310036, China;
d South China University of Technology, Guangzhou 510641, China

收稿日期:2011-12-02 修回日期:2012-06-11 出版日期:2012-09-01 发布日期:2012-09-01
基金资助:
Project supported by the Natural Science Foundation of Zhejiang Province of China (Grant Nos. Y1110766, Y1101316, Y6110317, and LY12A05003) and the Key Science and Technology Plan Program of Zhejiang Province, China (Grant No. 2010C13021).

A 2-stage strategy updating rule promotes cooperation in the prisoner's dilemma game

Fang Xiang-Sheng (方祥圣)^a, Zhu Ping (朱平)^b, Liu Run-Ran (刘润然)^c, Liu En-Yu (刘恩钰)^d, Wei Gui-Yi (魏贵义)^b

a Department of Information Science, Anhui Institute of Economic Management, Hefei 230059, China;
b Networking and Distributed Computing Laboratory, Zhejiang Gongshang University, Hangzhou 310018, China;
c Institute for Information Economy, Hangzhou Normal University, Hangzhou 310036, China;
d South China University of Technology, Guangzhou 510641, China

Received:2011-12-02 Revised:2012-06-11 Online:2012-09-01 Published:2012-09-01
Contact: Zhu Ping E-mail:jackyzhu@mail.zjgsu.edu.cn
Supported by:
Project supported by the Natural Science Foundation of Zhejiang Province of China (Grant Nos. Y1110766, Y1101316, Y6110317, and LY12A05003) and the Key Science and Technology Plan Program of Zhejiang Province, China (Grant No. 2010C13021).

摘要/Abstract

摘要： In this study, we propose a spatial prisoner's dilemma game model with a 2-stage strategy updating rule, and focus on the cooperation behavior of the system. In the first stage, i.e., the pre-learning stage, a focal player decides whether to update his strategy according to the pre-learning factor β and the payoff difference between himself and the average of his neighbors. If the player makes up his mind to update, he enters into the second stage, i.e., the learning stage, and adopts a strategy of a randomly selected neighbor according to the standard Fermi updating rule. The simulation results show that the cooperation level has a non-trivial dependence on the pre-learning factor. Generally, the cooperation frequency decreases as the pre-learning factor increases; but a high cooperation level can be obtained in the intermediate region of -3<β<-1. We then give some explanations via studying the co-action of pre-learning and learning. Our results may sharpen the understanding of the influence of the strategy updating rule on evolutionary games.

关键词: evolutionary game theory, strategy updating, social cooperation, prisoner's dilemma game

Abstract: In this study, we propose a spatial prisoner's dilemma game model with a 2-stage strategy updating rule, and focus on the cooperation behavior of the system. In the first stage, i.e., the pre-learning stage, a focal player decides whether to update his strategy according to the pre-learning factor β and the payoff difference between himself and the average of his neighbors. If the player makes up his mind to update, he enters into the second stage, i.e., the learning stage, and adopts a strategy of a randomly selected neighbor according to the standard Fermi updating rule. The simulation results show that the cooperation level has a non-trivial dependence on the pre-learning factor. Generally, the cooperation frequency decreases as the pre-learning factor increases; but a high cooperation level can be obtained in the intermediate region of -3<β<-1. We then give some explanations via studying the co-action of pre-learning and learning. Our results may sharpen the understanding of the influence of the strategy updating rule on evolutionary games.

Key words: evolutionary game theory, strategy updating, social cooperation, prisoner's dilemma game

中图分类号: (Dynamics of social systems)

87.23.Ge

89.75.Hc (Networks and genealogical trees) 05.10.-a (Computational methods in statistical physics and nonlinear dynamics)

方祥圣, 朱平, 刘润然, 刘恩钰, 魏贵义. A 2-stage strategy updating rule promotes cooperation in the prisoner's dilemma game[J]. 中国物理B, 2012, 21(10): 108702-108702.

Fang Xiang-Sheng (方祥圣), Zhu Ping (朱平), Liu Run-Ran (刘润然), Liu En-Yu (刘恩钰), Wei Gui-Yi (魏贵义). A 2-stage strategy updating rule promotes cooperation in the prisoner's dilemma game[J]. Chin. Phys. B, 2012, 21(10): 108702-108702.

参考文献 58

[1]	Von Neumann J and Morgenstern O 1944 Theory of Games and Economic Behavior (Princeton: Princeton University Press)
[2]	Maynard Smith J 1982 Evolution and the Theory of Games (Cambridge: Cambridge University Press)
[3]	Axelrod R 1984 The Evolution of Cooperation (New York: Basic Books)
[4]	Rapoport A and Chammah A 1965 Prisoner's Dilemma (Ann Arbor: University of Michigan Press)
[5]	Hofbauer J and Sigmund K 1998 Evolutionary Games and Population Dynamics (Cambridge: Cambridge University Press)
[6]	Hamilton W D 1964 J. Theor. Biol. 7 17
[7]	Nowak M A and Sigmund K 2005 Nature 437 1291
[8]	Traulsen A and Nowak M A 2006 Proc. Natl. Acad. Sci. USA 103 10952
[9]	Hauert C, De Monte S, Hofbauer J and Sigmund K 2002 Science 296 1129
[10]	Hauert C, Traulsen A, Brandt H, Nowak M A and Sigmund K 2007 Science 316 1905
[11]	Wang Z, Huang J H, Xu Z J and Zhang L Z 2010 Chin. Phys. B 19 100204
[12]	Nowak M A 2006 Evolutionary Dynamics: Exploring the Equations of Life (Cambridge, MA: Harvard University Press)
[13]	Nowak M A and May R M 1992 Nature 359 826
[14]	Szabó G and Fáth G 2007 Phys. Rep. 446 97
[15]	Perc M and Szolnoki A 2010 BioSystems 99 109
[16]	Gross T and Blasius B 2008 J. R. Soc. Interface 5 259
[17]	Albert R and Barabási A L 2002 Rev. Mod. Phys. 74 47
[18]	Newman M E J 2003 SIAM Rev. 45 167
[19]	Szabó G and Tóke C 1998 Phys. Rev. E 58 69
[20]	Doebeli M and Knowlton N 1998 Proc. Natl. Acad. Sci. 95 8676
[21]	Wang Z, Wang Z, Zhu X D and Arenzon J J 2012 Phys. Rev. E 85 011149
[22]	Hauert C and Doebeli M 2004 Nature 428 643
[23]	Szolnoki A, Perc M, Szabó G and Stark H U 2009 Phys. Rev. E 80 021901
[24]	Wang Z, Murks A, Du W B, Rong Z H and Perc M 2011 J. Theor. Bio. 277 19
[25]	Szolnoki A, Perc M and Szabó G 2009 Phys. Rev. E 80 056104
[26]	Wang Z, Xu Z J and Zhang L Z 2010 Chin. Phys. B 19 110201
[27]	Abramson G and Kuperman M 2001 Phys. Rev. E 63 030901(R)
[28]	Du W B, Cao X B, Zhao L and Zhou H 2009 Chin. Phys. Lett. 26 058701
[29]	Du W B, Cao X B and Yang H X 2010 Chin. Phys. B 19 010204
[30]	Yang H X, Gao K, Han X P and Wang B H 2008 Chin. Phys. B 17 2759
[31]	Wu Z X, Xu X J, Chen Y and Wang Y H 2005 Phys. Rev. E 71 037103
[32]	Ren J, Wang W X and Qi F 2007 Phys. Rev. E 75 045101(R)
[33]	Chen X J and Wang L 2008 Phys. Rev. E 71 017103
[34]	Wang Z, Szolnoki A and Perc M 2012 Europhys. Lett. 97 48001
[35]	Santos F C and Pacheco J M 2005 Phys. Rev. Lett. 95 098104
[36]	Rong Z H, Li X and Wang X F 2007 Phys. Rev. E 76 027101
[37]	Du W B, Cao X B, Zhao L and Hu M B 2009 Physica A 388 4509
[38]	Du W B, Cao X B, Hu M B, Yang H X and Zhou H 2009 Physica A 388 2215
[39]	Du W B, Cao X B and Hu M B 2009 Physica A 388 5005
[40]	Liu Y K, Li Z, Chen X J and Wang L 2009 Chin. Phys. B 18 2623
[41]	Cao X B, Du W B and Rong Z H 2010 Physica A 389 1273
[42]	Zimmermann M G, Egíluz V M and Miguel M S 2004 Phys. Rev. E 69 065102
[43]	Fu F, Hauert C, Nowak M A and Wang L 2008 Phys. Rev. E 78 026117
[44]	Zhang J, Wang W Y, Du W B and Cao X B 2011 Physica A 390 2251
[45]	Lin Y T, Yang H X, Wu Z X and Wang B H 2011 Physica A 390 77
[46]	Hu M B, Jiang R, Wu Q S and Wu Y H 2007 Physica A 381 467
[47]	Wu Z X, Xu Z J, Huang Z G, Wang S J and Wang Y H 2006 Phys. Rev. E 74 021107
[48]	Wang W X, Ren J, Chen G R and Wang B H 2006 Phys. Rev. E 74 056113
[49]	Gao K, Wang W X and Wang B H 2007 Physica A 380 528
[50]	Wang Z, Szolnoki A and Perc M 2012 Sci. Rep. 2 369 DOI: 10.1038/srep00369
[51]	Nowak M A and Sigmund K 1993 Nature 364 56
[52]	Zhang J, Fang Y P, Du W B and Cao X B 2011 Physica A 390 2258
[53]	Nowak M A and May R M 1993 Int. J. Bifur. Chaos Appl. Sci. Eng. 3 35
[54]	Jin Q, Wang Z, Wang Z and Wang Y L 2012 Chaos, Solitons and Fractals 45 395
[55]	Wang Z, Du W B, Cao X B and Zhang L Z 2011 Physica A 390 1234
[56]	Szabó G, Vukov J and Szolnoki A 2005 Phys. Rev. E 72 047107
[57]	Vukov J, Szabó G and Szolnoki A 2006 Phys. Rev. E 73 067103
[58]	Newman M E J and Watts D J 1999 Phys. Rev. E 60 7332

A 2-stage strategy updating rule promotes cooperation in the prisoner's dilemma game

A 2-stage strategy updating rule promotes cooperation in the prisoner's dilemma game

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